Legal Question in Landlord & Tenant Law in California

They are. When you buy a property you step into the exact set of legal rights and responsibilities as the prior owner. You are subject to any easements. You are subject to any liens that are not paid off at the time you acquire the property, and you step into the exact legal position as the former owner as to any leases. Since the former owner had no legal right to demand any further rent payments before the lease is up, neither do you. On top of that, you owe the deposit (less any legal deductions for damage) at the end of the lease. The only exception to this rule is if the buyer genuinely and in good faith had no idea the occupant was a tenant and truly and with legitimate reason believed the occupant was the former owner. In that case you may be a "bona fide purchaser for value without notice," which would mean your ownership is clear of any claims not shown in the county recorder's land title records. If you think you have that situation and clear evidence to prove it, you should contact an experienced real estate litigation attorney for a full evaluation of your case.

The tenant has a strong argument that you need to seek the rent from the former owner. I believe the analysis is similar to the security deposit issue in which the former owner is suppose to give the deposit to you or do a disposition and return the balance to the tenant. If the former owner does neither regarding the deposit, you are responsible for accounting for/returning the deposit at the end of the tenancy even though you never actually received the funds from the former owner. I would say that, if the tenant can prove that the rent was paid in advance, you need to go after the rent from the former owner.